Abstract

Employing the common property (E.A), we prove some
common fixed point theorems for weakly compatible mappings via an implicit relation
in Menger PM spaces. Some results on similar lines satisfying quasicontraction
condition as well as ψ-type contraction condition are also proved in Menger PM
spaces. Our results substantially improve the corresponding theorems contained in
(Branciari, (2002); Rhoades, (2003); Vijayaraju et al., (2005)) and also some others in Menger as well as metric spaces. Some related
results are also derived besides furnishing illustrative examples.